Math Problem Statement
Consider the ANOVA table that follows.
Analysis of Variance Source DF SS MS F Regression 5 4,001.11 800.22 14.72 Residual Error 48 2,610.04 54.38 Total 53 6,611.16 Standard error of estimate 7.37 About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.)
Solution
To solve this problem, we can use the information provided in the ANOVA table, particularly the standard error of the estimate (which is 7.37). Since about 95% of the residuals are expected to fall within ±1.96 standard deviations (based on the properties of a normal distribution), we will compute the following:
Let's calculate this:
Thus, about 95% of the residuals will be between:
So, the residuals will fall between -14.44 and 14.44.
Would you like any further details or have any questions?
Here are 5 related questions you might find interesting:
- How is the standard error of the estimate calculated in regression analysis?
- Why do we use 1.96 standard deviations for a 95% confidence interval?
- What is the relationship between residuals and the accuracy of a regression model?
- How does an increase in residual variance affect the model's predictions?
- How would you interpret an ANOVA table with a different F-value?
Tip: Always check the assumptions of normality and homoscedasticity when interpreting residuals in regression models.
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Math Problem Analysis
Mathematical Concepts
ANOVA
Regression Analysis
Confidence Interval
Standard Error
Formulas
Range of residuals = ±1.96 × Standard Error of Estimate
Theorems
Normal distribution (95% confidence interval covers ±1.96 standard deviations)
Suitable Grade Level
College level
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